Open Access
2013 Persistence and Nonpersistence of a Nonautonomous Stochastic Mutualism System
Peiyan Xia, Xiaokun Zheng, Daqing Jiang
Abstr. Appl. Anal. 2013(SI21): 1-13 (2013). DOI: 10.1155/2013/256249


In this paper, a two-species nonautonomous stochastic mutualism system is investigated. The intrinsic growth rates of the two species at time t are estimated by r i t + σ i t B ˙ i ( t ) , i = 1,2, respectively. Viewing the different intensities of the noises σ i ( t ) , i = 1 , 2 as two parameters at time t , we conclude that there exists a global positive solution and the p th moment of the solution is bounded. We also show that the system is permanent, including stochastic permanence, persistence in mean, and asymptotic boundedness in time average. Besides, we show that the large white noise will make the system nonpersistent. Finally, we establish sufficient criteria for the global attractivity of the system.


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Peiyan Xia. Xiaokun Zheng. Daqing Jiang. "Persistence and Nonpersistence of a Nonautonomous Stochastic Mutualism System." Abstr. Appl. Anal. 2013 (SI21) 1 - 13, 2013.


Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 06161315
MathSciNet: MR3034979
Digital Object Identifier: 10.1155/2013/256249

Rights: Copyright © 2013 Hindawi

Vol.2013 • No. SI21 • 2013
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